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Sholpan [36]
3 years ago
14

The snowboard Hannah wanted originally cost $109.It had been marked down 10% and then another 12%. A tax of 6% was added to the

final sale price. If Hannah had $90, did she have enough to buy the snowboard? Explain your answer.
Answer:
Mathematics
1 answer:
lara [203]3 years ago
5 0

Take 10% of the snowboard price.

10% = 0.1

109 * 0.1 = $10.90 (10% discount)

109 - 10.9 = $98.10 (Price with discount).

Take 12% of the new snowboard price.

12% = 0.12

98.1 * 0.12 = 11.772 (Round to 11.77)

98.10 - 11.77 = $86.33 (Final discounted price)

Take 6% tax on the new snowboard price.

6% = 0.06

86.33 * 0.06 = 5.1798 (Round to 5.18)

86.33 + 5.18 = $91.51

______

After solving Hannah doesn't have enough money to buy the snowboard.

______

Best Regards,

Wolfyy :)

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GenaCL600 [577]

The measure of angle ABC is 45°

<em><u>Explanation</u></em>

Vertices of the triangle are:   A(7, 5), B(4, 2), and C(9, 2)

According to the diagram below....

Length of the side BC (a) =\sqrt{(4-9)^2+(2-2)^2}= \sqrt{25}= 5

Length of the side AC (b) = \sqrt{(7-9)^2 +(5-2)^2}= \sqrt{4+9}=\sqrt{13}

Length of the side AB (c) = \sqrt{(7-4)^2 +(5-2)^2} =\sqrt{9+9}=\sqrt{18}

We need to find ∠ABC or ∠B . So using <u>Cosine rule</u>, we will get...

cosB= \frac{a^2+c^2-b^2}{2ac} \\ \\ cos B= \frac{(5)^2+(\sqrt{18})^2-(\sqrt{13})^2}{2*5*\sqrt{18} }\\ \\ cosB= \frac{25+18-13}{10\sqrt{18}} =\frac{30}{10\sqrt{18}}=\frac{3}{\sqrt{18}}\\ \\ cosB=\frac{3}{3\sqrt{2}} =\frac{1}{\sqrt{2}}\\ \\ B= cos^-^1(\frac{1}{\sqrt{2}})= 45 degree

So, the measure of angle ABC is 45°

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